Bligh's Theory of Hydraulic Structures
Lecture-2
Bligh's Theory
This is also known as a
creep theory, and the length of the path that the seeping water moves is known
as the creep length or the length of creep. The head loss happens as the water
moves slowly from the upstream end to the downstream end. The creep distance
traveled is proportionate to the head loss. According to Bligh, Water
percolates, or seeps, along the base profile of the structure that is in
contact with the subsoil in a prior foundation. Creep length (Lw) is the length
of the seepage path that the water flows. Additionally, the loss of head (HL)
per unit length of creep, or the subsoil hydraulic gradient, remains
constant along the seepage path.
The hydraulic gradient is
the loss of head per unit length equal to HL/Lw, HL is the total head loss
or seepage head, which is the difference in water levels between the upstream
and downstream ends, and Lw is the entire creep length.
Figure:
Bligh's Creep [Image Source: From online]
Lw = 2d1 + L1 + 2d3 + L2 + 2d2
Where d1, d2,
and d3 are the depths of the upstream, downstream and intermediate piles
respectively. l1 and l2 are the lengths between the upstream and
downstream piles.
The head loss per unit
length or hydraulic gradient is given by:
where, HL = HU/S – H D/S
= difference in water levels between u/s and d/s ends,
HU/S = water depth at U/S
end, and
HD/S =
water depth at D/S end.
The subsurface hydraulic
gradient lines in Figure below illustrate the pressure heads caused by
subsurface (seepage) flow at the location under the impervious floor.
Additionally, the subsurface hydraulic gradient line at the pile locations
(cutoffs) abruptly drops in the figure.
Figure: Bligh's Creep [Image Source: From online]
Head loss occurs on
upstream cutoff = HL/Lw * (2d1)
Head loss occurs on
intermediate cutoff = HL/Lw * (2d2)
Head loss occurs on
downstream cutoff = HL/Lw * (2d3)
Head at Point C = Total
Head – Head loss occurs on U/S cutoff
Safety against
piping
The hydraulic gradient of the seepage flow beneath the floor's base is known as the exit gradient. As the exit gradient rises, the rate of seepage also rises, which would lead to the "boiling" of surface soil as the percolating water washes the soil far away. More soil is removed when the flow concentrates into the resulting depression, causing gradual scour upstream. The foundations are eventually undermined by this "piping" development. The subsoil hydraulic gradient must be less than the allowable value in order to prevent piping failure and ensure the safety of the hydraulic structure on a pervious base. If the hydraulic gradient is at or below a safe level, piping failure won't happen.
By decreasing the exit
gradient, or lengthening the creep, the piping phenomena can be reduced.
Increasing the length of the impermeable floor and installing upstream and
downstream cut-off piles will lengthen the creep.
For a safe design,
Where, C1 is Bligh's creep coefficient, which
depends upon the type of soil.
Table: Bligh's
Creep Coefficient
|
Sl.
No. |
Type
of soil |
Creep
coefficient, C1 |
Safe
hydraulic gradient, 1/C1, should be less than |
|
1. |
Light
sand and mud |
8 |
1/8 |
|
2 |
Fine
micaceous sand |
15 |
1/15 |
|
3 |
Coarse
grained sand |
12 |
1/12 |
|
4 |
Boulders
and gravel mixed with sand |
5-9 |
1/5
to 1/9 |
Safety against Uplift Pressures
The impervious floor's
base is affected by uplift pressures from water seeping beneath the floor. The
floor should be thick enough to prevent rupture due to uplift pressure. If the
floor's weight is insufficient, it may crack or rupture, reducing the floor's
effective length and increasing the exit gradient. To prevent failure,
increased creep lengths and sufficient floor thickness are recommended.
Excessively thick foundations are costly to construct below the river bed, so
piers can be extended and thin reinforced concrete floors provided between them
to resist failure by bending.
Figure:
Bligh's Uplift Pressure [Image
Source: From online]
The residual head, h at
any point p is:
where l is the
horizontal length between point A and p.
Again, h' = h + t, where
t is the thickness of floor.
The upward force, F
acting on the unit area of the floor due to uplift pressure is given by:
F = PA = γw
h’A = γw (h+t
) x 1,
A = unit area = 1, γw
= specific weight of water.
The downward force W due
to the weight of the floor material is given by:
W= Gf x γw
x V = Gf x
γw
x A x t = Gf x
γw
x 1 x t
Equating
F = W
γw (h+t) x1 = Gf
x γw x 1 x t
γw (h+t) = Gf x γw x t
t = h/(Gf-1)
In general, a factor of
safety 4/3 is adopted. Thus
t =4/3 * [ h/(Gf-1)]
Limitations of Bligh's Theory
·
The Bligh theory does not differentiate
between the vertical creep and the horizontal
·
creep and gives the same weightage to both.
·
The theory assumes a linear variation of
the head loss, but head loss variation is non-linear.
·
No difference is made between the head
loss on the outer faces and that on the inner faces of the sheet piles.
·
The theory overlooks the downstream pile's
role in piping failure, viewing it as a component of total creep length rather
than a controlling factor for exit gradient and piping.
·
The theory does not give any theoretical
or practical method for the determination of
·
the creep coefficient C1.
·
Bligh did not consider the effect of the
intermediary pile.
· The theory does not produce the approximate findings if the horizontal distance between the piles is less than twice their depths.
Example 1:
A hydraulic structure
built on fine sand (C1 = 15). Use Bligh's theory. Take Gf = 2.5. Determine:
a) Hydraulic
gradient is safe or not.
b) Uplift
pressure at points A, B, and C at distances 10, 20, and 35 m from the upstream
end.
c) Thickness
of floor at these points.
Solution:
(a)
(b)
(c)
Thickness of floor,
Homework’s
1.
Find the hydraulic gradient and uplift
pressure and the thickness of floor at a point C, 15 m from the upstream end of
the floor in the Figure below. All dimensions in meter.
2. Find
the hydraulic gradient and the head at point D of the following structure for
static condition.
